The solution of the linear regression problem in Eq. (REF ) is a
crucial step. The standard methods used for training MLFFs are based on ridge
regression, where a regularization parameter \(\sigma _\textup {v}^2/\sigma _\textup {w}^2\)  is introduced [1]}. In the probabilistic
framework of Bayesian linear regression (BLR) adopted here, the coefficients
are formally determined in the same way:
\( \mathbf {w} = \left( \mathbf {\Phi }^\textup {T}\mathbf {\Phi }+ \sigma _\textup {v}^2/\sigma _\textup {w}^2\, \mathbf {I} \right)^{-1} \mathbf {\Phi }^\textup {T} \mathbf {y},\) 
